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Mat. Sb., 2008, Volume 199, Number 2, Pages 93–114 (Mi msb3685)  

This article is cited in 19 scientific papers (total in 19 papers)

Best approximations and widths of classes of periodic functions of several variables

A. S. Romanyuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: Order estimates are obtained for the best approximations of the Besov classes $B_{p,\theta}^r$ of periodic functions of several variables in the spaces $L_1$ and $L_\infty$ by trigonometric polynomials whose harmonic indices lie in step hyperbolic crosses. The orders of the orthoprojection widths of the classes $B_{p,\theta}^r$ and the linear widths of the classes $B_{p,\theta}^r$ and $W_{p,\alpha}^r$ in the space $L_1$ are found.
Bibliography: 22 titles.

DOI: https://doi.org/10.4213/sm3685

Full text: PDF file (618 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:2, 253–275

Bibliographic databases:

UDC: 517.51
MSC: 41A46, 41A45, 41A50
Received: 12.09.2006 and 19.11.2007

Citation: A. S. Romanyuk, “Best approximations and widths of classes of periodic functions of several variables”, Mat. Sb., 199:2 (2008), 93–114; Sb. Math., 199:2 (2008), 253–275

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. A. Bekmaganbetov, “O poryadkakh priblizheniya klassa Besova v metrike anizotropnykh prostranstv Lorentsa”, Ufimsk. matem. zhurn., 1:2 (2009), 9–16  mathnet  zmath  elib
    2. D. B. Bazarkhanov, “Estimates of the Fourier Widths of Classes of Nikolskii–Besov and Lizorkin–Triebel Types of Periodic Functions of Several Variables”, Math. Notes, 87:2 (2010), 281–284  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. S. Romanyuk, “Approximation of Classes $B^r_{p,\theta}$ of Periodic Functions of One and Several Variables”, Math. Notes, 87:3 (2010), 403–415  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. D. B. Bazarkhanov, “Wavelet approximation and Fourier widths of classes of periodic functions of several variables. I”, Proc. Steklov Inst. Math., 269 (2010), 2–24  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. Dũng D., “B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness”, Journal of Complexity, 27:6 (2011), 541–567  crossref  mathscinet  zmath  isi  scopus
    6. Sickel W., Ullrich T., “Spline interpolation on sparse grids”, Appl. Anal., 90:3-4 (2011), 337–383  crossref  mathscinet  zmath  isi  elib  scopus
    7. Romanyuk A.S., “Poperechniki i nailuchshee priblizhenie klassov $B^r_{p,\theta}$ periodicheskikh funktsii mnogikh peremennykh”, Anal. Math., 37:3 (2011), 181–213  crossref  mathscinet  zmath  isi  scopus
    8. S. A. Stasyuk, “Nailuchshee priblizhenie periodicheskikh funktsii neskolkikh peremennykh iz klassov $MB^\omega_{p,\theta}$ v ravnomernoi metrike”, Tr. IMM UrO RAN, 18, no. 4, 2012, 258–266  mathnet  elib
    9. Hansen M., Sickel W., “Best $m$-term approximation and Sobolev–Besov spaces of dominating mixed smoothness—the case of compact embeddings”, Constr. Approx., 36:1 (2012), 1–51  crossref  mathscinet  zmath  isi  elib  scopus
    10. Stasyuk S.A., “Best approximation of periodic functions of several variables from the classes $MB_{p,\theta}^\omega$”, Ukr. Math. J., 64:1 (2012), 156–161  crossref  mathscinet  zmath  isi  elib  scopus
    11. A. F. Konograj, “Estimates of the Approximation Characteristics of the Classes $B^{\Omega}_{p,\theta}$ of Periodic Functions of Several Variables with Given Majorant of Mixed Moduli of Continuity”, Math. Notes, 95:5 (2014), 656–669  mathnet  crossref  crossref  mathscinet  isi  elib
    12. Romanyuk A.S., “On the Problem of Linear Widths of the Classes B (P,Theta) (R) of Periodic Functions of Many Variables”, Ukr. Math. J., 66:7 (2014), 1085–1098  crossref  mathscinet  zmath  isi  scopus
    13. Van Kien Nguyen, Sickel W., “Weyl Numbers of Embeddings of Tensor Product Besov Spaces”, J. Approx. Theory, 200 (2015), 170–220  crossref  mathscinet  zmath  isi  scopus
    14. Bazarkhanov D.B., “Fourier widths of some function classes associated with m–multiple Haar system”, INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016) (Almaty, Kazakhstan, 7–10 September 2016), AIP Conference Proceedings, 1759, ed. Ashyralyev A. Lukashov A., Amer Inst Physics, 2016, 020110  crossref  isi  scopus
    15. K. A. Bekmaganbetov, Ye. Toleugazy, “Order of the orthoprojection widths of the anisotropic Nikol'skii–Besov classes in the anisotropic Lorentz space”, Eurasian Math. J., 7:3 (2016), 8–16  mathnet  mathscinet
    16. Van Kien Nguyen, “Gelfand Numbers of Embeddings of Mixed Besov Spaces”, J. Complex., 41 (2017), 35–57  crossref  mathscinet  zmath  isi  scopus
    17. Romanyuk A.S., “Entropy Numbers and Widths For the Classes of Periodic Functions of Many Variables”, Ukr. Math. J., 68:10 (2017), 1620–1636  crossref  mathscinet  isi  scopus
    18. Byrenheid G., Ullrich T., “Optimal Sampling Recovery of Mixed Order Sobolev Embeddings Via Discrete Littlewood-Paley Type Characterizations”, Anal. Math., 43:2 (2017), 133–191  crossref  mathscinet  zmath  isi  scopus
    19. Romanyuk A.S., “Trigonometric and Linear Widths For the Classes of Periodic Multivariate Functions”, Ukr. Math. J., 69:5 (2017), 782–795  crossref  mathscinet  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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